Convergence of optimal prediction for nonlinear Hamiltonian systems

Ole H. Hald*, Raz Kupferman

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

6 Scopus citations


Optimal prediction is a computational method for systems that cannot be properly resolved, in which the unresolved variables are viewed as random. This paper presents a first analysis of optimal prediction as a numerical method. We prove the convergence of the scheme for a class of equations of Schrödinger type and derive error bounds for the mean error between the optimal prediction solution and the set of exact solutions with random initial data. It is shown that optimal prediction is the scheme that minimizes the mean truncation error.

Original languageAmerican English
Pages (from-to)983-1000
Number of pages18
JournalSIAM Journal on Numerical Analysis
Issue number3
StatePublished - 2002


  • Nonlinear Schrödinger
  • Optimal prediction
  • Statistical mechanics


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